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pashok25 [27]
2 years ago
15

2) Abby made 5 1/2 cups of banana pudding. She served 7/8 cup of the pudding to her kids for dessert.

Mathematics
1 answer:
frez [133]2 years ago
3 0

Answer:

<u>37/8</u>

Step-by-step explanation:

we are going to create 5 1/2 into an improper fraction for now, so it is easier to manipulate.

5 1/2 = 11/10

in order to find the answer, we need to set them both to a common denominator(we need to make sure they have the same denominator so it is easier to subtract)

11/2 if we just take 1 of the cups that Abby made and subtract that by 7/8 that give us the answer

11/2 - 1 = 9/2

we will now us the cup we subtracted from that and "give it to the kids"

 1 = 8/8

so

8/8 - 7/8 = 1/8

so we have 1/8 leftover from that cup, so we can add that back

since 1/8 is a hard number to just add off the top of your head, we can just change the denominator of 9/2 into 8 instead of 2:

9/2 = 36/8

so

1/8 + 36/8 = 37/8

so since 37/8 cannot be simplified anymore, the answer is

<u>37/8</u>

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Step-by-step explanation:

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(a) Find the size of each of two samples (assume that they are of equal size) needed to estimate the difference between the prop
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Answer:

(a) The sample sizes are 6787.

(b) The sample sizes are 6666.

Step-by-step explanation:

(a)

The information provided is:

Confidence level = 98%

MOE = 0.02

n₁ = n₂ = n

\hat p_{1} = \hat p_{2} = \hat p = 0.50\ (\text{Assume})

Compute the sample sizes as follows:

MOE=z_{\alpha/2}\times\sqrt{\frac{2\times\hat p(1-\hat p)}{n}

       n=\frac{2\times\hat p(1-\hat p)\times (z_{\alpha/2})^{2}}{MOE^{2}}

          =\frac{2\times0.50(1-0.50)\times (2.33)^{2}}{0.02^{2}}\\\\=6786.125\\\\\approx 6787

Thus, the sample sizes are 6787.

(b)

Now it is provided that:

\hat p_{1}=0.45\\\hat p_{2}=0.58

Compute the sample size as follows:

MOE=z_{\alpha/2}\times\sqrt{\frac{\hat p_{1}(1-\hat p_{1})+\hat p_{2}(1-\hat p_{2})}{n}

       n=\frac{(z_{\alpha/2})^{2}\times [\hat p_{1}(1-\hat p_{1})+\hat p_{2}(1-\hat p_{2})]}{MOE^{2}}

          =\frac{2.33^{2}\times [0.45(1-0.45)+0.58(1-0.58)]}{0.02^{2}}\\\\=6665.331975\\\\\approx 6666

Thus, the sample sizes are 6666.

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The triangle shown is an isosceles triangle because it has two congruent sides. The base angles of isosceles triangles are congruent so ∠y=∠x. since the ∠x is 52 the ∠y is also 52. We subtract the measure of angles x and y in order to find the measure of the third angle. 180-(52+52) or 180-104 is 76. this means that 14x=6=76. All we have to do to get the answer now is solve. 76-6 is 70 and 70 divided by 14 is 5. x=5.

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